{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "import numpy as np\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Main code for Concrete Dropout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Couldn't import dot_parser, loading of dot files will not be possible.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import keras.backend as K\n",
    "from keras import initializers\n",
    "from keras.engine import InputSpec\n",
    "from keras.layers import Dense, Lambda, Wrapper\n",
    "\n",
    "\n",
    "class ConcreteDropout(Wrapper):\n",
    "    \"\"\"This wrapper allows to learn the dropout probability for any given input layer.\n",
    "    ```python\n",
    "        # as the first layer in a model\n",
    "        model = Sequential()\n",
    "        model.add(ConcreteDropout(Dense(8), input_shape=(16)))\n",
    "        # now model.output_shape == (None, 8)\n",
    "        # subsequent layers: no need for input_shape\n",
    "        model.add(ConcreteDropout(Dense(32)))\n",
    "        # now model.output_shape == (None, 32)\n",
    "    ```\n",
    "    `ConcreteDropout` can be used with arbitrary layers, not just `Dense`,\n",
    "    for instance with a `Conv2D` layer:\n",
    "    ```python\n",
    "        model = Sequential()\n",
    "        model.add(ConcreteDropout(Conv2D(64, (3, 3)),\n",
    "                                  input_shape=(299, 299, 3)))\n",
    "    ```\n",
    "    # Arguments\n",
    "        layer: a layer instance.\n",
    "        weight_regularizer:\n",
    "            A positive number which satisfies\n",
    "                $weight_regularizer = l**2 / (\\tau * N)$\n",
    "            with prior lengthscale l, model precision $\\tau$ (inverse observation noise),\n",
    "            and N the number of instances in the dataset.\n",
    "            Note that kernel_regularizer is not needed.\n",
    "        dropout_regularizer:\n",
    "            A positive number which satisfies\n",
    "                $dropout_regularizer = 2 / (\\tau * N)$\n",
    "            with model precision $\\tau$ (inverse observation noise) and N the number of\n",
    "            instances in the dataset.\n",
    "            Note the relation between dropout_regularizer and weight_regularizer:\n",
    "                $weight_regularizer / dropout_regularizer = l**2 / 2$\n",
    "            with prior lengthscale l. Note also that the factor of two should be\n",
    "            ignored for cross-entropy loss, and used only for the eculedian loss.\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, layer, weight_regularizer=1e-6, dropout_regularizer=1e-5,\n",
    "                 init_min=0.1, init_max=0.1, is_mc_dropout=True, **kwargs):\n",
    "        assert 'kernel_regularizer' not in kwargs\n",
    "        super(ConcreteDropout, self).__init__(layer, **kwargs)\n",
    "        self.weight_regularizer = weight_regularizer\n",
    "        self.dropout_regularizer = dropout_regularizer\n",
    "        self.is_mc_dropout = is_mc_dropout\n",
    "        self.supports_masking = True\n",
    "        self.p_logit = None\n",
    "        self.p = None\n",
    "        self.init_min = np.log(init_min) - np.log(1. - init_min)\n",
    "        self.init_max = np.log(init_max) - np.log(1. - init_max)\n",
    "\n",
    "    def build(self, input_shape=None):\n",
    "        self.input_spec = InputSpec(shape=input_shape)\n",
    "        if not self.layer.built:\n",
    "            self.layer.build(input_shape)\n",
    "            self.layer.built = True\n",
    "        super(ConcreteDropout, self).build()  # this is very weird.. we must call super before we add new losses\n",
    "\n",
    "        # initialise p\n",
    "        self.p_logit = self.layer.add_weight(name='p_logit',\n",
    "                                            shape=(1,),\n",
    "                                            initializer=initializers.RandomUniform(self.init_min, self.init_max),\n",
    "                                            trainable=True)\n",
    "        self.p = K.sigmoid(self.p_logit[0])\n",
    "\n",
    "        # initialise regulariser / prior KL term\n",
    "        input_dim = np.prod(input_shape[1:])  # we drop only last dim\n",
    "        weight = self.layer.kernel\n",
    "        kernel_regularizer = self.weight_regularizer * K.sum(K.square(weight)) / (1. - self.p)\n",
    "        dropout_regularizer = self.p * K.log(self.p)\n",
    "        dropout_regularizer += (1. - self.p) * K.log(1. - self.p)\n",
    "        dropout_regularizer *= self.dropout_regularizer * input_dim\n",
    "        regularizer = K.sum(kernel_regularizer + dropout_regularizer)\n",
    "        self.layer.add_loss(regularizer)\n",
    "\n",
    "    def compute_output_shape(self, input_shape):\n",
    "        return self.layer.compute_output_shape(input_shape)\n",
    "\n",
    "    def concrete_dropout(self, x):\n",
    "        '''\n",
    "        Concrete dropout - used at training time (gradients can be propagated)\n",
    "        :param x: input\n",
    "        :return:  approx. dropped out input\n",
    "        '''\n",
    "        eps = K.cast_to_floatx(K.epsilon())\n",
    "        temp = 0.1\n",
    "\n",
    "        unif_noise = K.random_uniform(shape=K.shape(x))\n",
    "        drop_prob = (\n",
    "            K.log(self.p + eps)\n",
    "            - K.log(1. - self.p + eps)\n",
    "            + K.log(unif_noise + eps)\n",
    "            - K.log(1. - unif_noise + eps)\n",
    "        )\n",
    "        drop_prob = K.sigmoid(drop_prob / temp)\n",
    "        random_tensor = 1. - drop_prob\n",
    "\n",
    "        retain_prob = 1. - self.p\n",
    "        x *= random_tensor\n",
    "        x /= retain_prob\n",
    "        return x\n",
    "\n",
    "    def call(self, inputs, training=None):\n",
    "        if self.is_mc_dropout:\n",
    "            return self.layer.call(self.concrete_dropout(inputs))\n",
    "        else:\n",
    "            def relaxed_dropped_inputs():\n",
    "                return self.layer.call(self.concrete_dropout(inputs))\n",
    "            return K.in_train_phase(relaxed_dropped_inputs,\n",
    "                                    self.layer.call(inputs),\n",
    "                                    training=training)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluate Concrete Dropout on synthetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Ns = [10, 25, 50, 100, 1000, 10000]\n",
    "Ns = np.array(Ns)\n",
    "nb_epochs = [2000, 1000, 500, 200, 20, 2]\n",
    "nb_val_size = 1000\n",
    "nb_features = 1024\n",
    "Q = 1\n",
    "D = 1\n",
    "K_test = 20\n",
    "nb_reps = 3\n",
    "batch_size = 20\n",
    "l = 1e-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def gen_data(N):\n",
    "    sigma = 1e0  # ground truth\n",
    "    X = np.random.randn(N, Q)\n",
    "    w = 2.\n",
    "    b = 8.\n",
    "    Y = X.dot(w) + b + sigma * np.random.randn(N, D)\n",
    "    return X, Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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     "output_type": "display_data"
    },
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OKqXeBhCRp3A3i73iBgOu0cDMtlbwIlClezi+9zd3T9ur2MuheF1ciqpgr1py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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42f5c74e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab\n",
    "%matplotlib inline\n",
    "\n",
    "X, Y = gen_data(10)\n",
    "pylab.figure(figsize=(3, 1.5))\n",
    "pylab.scatter(X[:, 0], Y[:, 0], edgecolor='b')\n",
    "pylab.savefig('data_10.pdf', bbox_inches='tight')\n",
    "pylab.show()\n",
    "\n",
    "X, Y = gen_data(10000)\n",
    "pylab.figure(figsize=(3, 1.5))\n",
    "pylab.scatter(X[:, 0], Y[:, 0], edgecolor='b')\n",
    "pylab.xlim([-5, 5])\n",
    "pylab.ylim([-2, 20])\n",
    "pylab.savefig('data_10000.pdf', bbox_inches='tight')\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from keras.layers import Input, Dense, Lambda, merge\n",
    "from keras.models import Model\n",
    "from keras import backend as K\n",
    "\n",
    "def fit_model(nb_epoch, X, Y):\n",
    "    if K.backend() == 'tensorflow':\n",
    "        K.clear_session()\n",
    "    N = X.shape[0]\n",
    "    wd = l**2. / N\n",
    "    dd = 2. / N\n",
    "    inp = Input(shape=(Q,))\n",
    "    x = inp\n",
    "    x = ConcreteDropout(Dense(nb_features, activation='relu'), weight_regularizer=wd, dropout_regularizer=dd)(x)\n",
    "    x = ConcreteDropout(Dense(nb_features, activation='relu'), weight_regularizer=wd, dropout_regularizer=dd)(x)\n",
    "    x = ConcreteDropout(Dense(nb_features, activation='relu'), weight_regularizer=wd, dropout_regularizer=dd)(x)\n",
    "    mean = ConcreteDropout(Dense(D), weight_regularizer=wd, dropout_regularizer=dd)(x)\n",
    "    log_var = ConcreteDropout(Dense(D), weight_regularizer=wd, dropout_regularizer=dd)(x)\n",
    "    out = merge([mean, log_var], mode='concat')\n",
    "    model = Model(inp, out)\n",
    "    \n",
    "    def heteroscedastic_loss(true, pred):\n",
    "        mean = pred[:, :D]\n",
    "        log_var = pred[:, D:]\n",
    "        precision = K.exp(-log_var)\n",
    "        return K.sum(precision * (true - mean)**2. + log_var, -1)\n",
    "    \n",
    "    model.compile(optimizer='adam', loss=heteroscedastic_loss)\n",
    "    assert len(model.layers[1].trainable_weights) == 3  # kernel, bias, and dropout prob\n",
    "    assert len(model.losses) == 5  # a loss for each Concrete Dropout layer\n",
    "    hist = model.fit(X, Y, nb_epoch=nb_epoch, batch_size=batch_size, verbose=0)\n",
    "    loss = hist.history['loss'][-1]\n",
    "    return model, -0.5 * loss  # return ELBO up to const."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eval function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def logsumexp(a):\n",
    "    a_max = a.max(axis=0)\n",
    "    return np.log(np.sum(np.exp(a - a_max), axis=0)) + a_max\n",
    "\n",
    "def test(Y_true, MC_samples):\n",
    "    \"\"\"\n",
    "    Estimate predictive log likelihood:\n",
    "    log p(y|x, D) = log int p(y|x, w) p(w|D) dw\n",
    "                 ~= log int p(y|x, w) q(w) dw\n",
    "                 ~= log 1/K sum p(y|x, w_k) with w_k sim q(w)\n",
    "                  = LogSumExp log p(y|x, w_k) - log K\n",
    "    :Y_true: a 2D array of size N x dim\n",
    "    :MC_samples: a 3D array of size samples K x N x 2*D\n",
    "    \"\"\"\n",
    "    assert len(MC_samples.shape) == 3\n",
    "    assert len(Y_true.shape) == 2\n",
    "    k = MC_samples.shape[0]\n",
    "    N = Y_true.shape[0]\n",
    "    mean = MC_samples[:, :, :D]  # K x N x D\n",
    "    logvar = MC_samples[:, :, D:]\n",
    "    test_ll = -0.5 * np.exp(-logvar) * (mean - Y_true[None])**2. - 0.5 * logvar - 0.5 * np.log(2 * np.pi)\n",
    "    test_ll = np.sum(np.sum(test_ll, -1), -1)\n",
    "    test_ll = logsumexp(test_ll) - np.log(k)\n",
    "    pppp = test_ll / N  # per point predictive probability\n",
    "    rmse = np.mean((np.mean(mean, 0) - Y_true)**2.)**0.5\n",
    "    return pppp, rmse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot function to make sure stuff makes sense:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot(X_train, Y_train, X_val, Y_val, means):\n",
    "    indx = np.argsort(X_val[:, 0])\n",
    "    _, (ax1, ax2, ax3, ax4) = pylab.subplots(1, 4,figsize=(12, 1.5), sharex=True, sharey=True)\n",
    "    ax1.scatter(X_train[:, 0], Y_train[:, 0], c='y')\n",
    "    ax1.set_title('Train set')\n",
    "    ax2.plot(X_val[indx, 0], np.mean(means, 0)[indx, 0], color='skyblue', lw=3)\n",
    "    ax2.scatter(X_train[:, 0], Y_train[:, 0], c='y')\n",
    "    ax2.set_title('+Predictive mean')\n",
    "    for mean in means:\n",
    "        ax3.scatter(X_val[:, 0], mean[:, 0], c='b', alpha=0.2, lw=0)\n",
    "    ax3.plot(X_val[indx, 0], np.mean(means, 0)[indx, 0], color='skyblue', lw=3)\n",
    "    ax3.set_title('+MC samples on validation X')\n",
    "    ax4.scatter(X_val[:, 0], Y_val[:, 0], c='r', alpha=0.2, lw=0)\n",
    "    ax4.set_title('Validation set')\n",
    "    pylab.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Run experiment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/IPython/kernel/__main__.py:18: UserWarning: The `merge` function is deprecated and will be removed after 08/2017. Use instead layers from `keras.layers.merge`, e.g. `add`, `concatenate`, etc.\n",
      "/usr/local/lib/python2.7/dist-packages/keras/legacy/layers.py:460: UserWarning: The `Merge` layer is deprecated and will be removed after 08/2017. Use instead layers from `keras.layers.merge`, e.g. `add`, `concatenate`, etc.\n",
      "  name=name)\n",
      "/usr/local/lib/python2.7/dist-packages/IPython/kernel/__main__.py:28: UserWarning: The `nb_epoch` argument in `fit` has been renamed `epochs`.\n"
     ]
    },
    {
     "data": {
      "image/png": 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vampcOlr2GEYYnx5xMvBVYMLO+RHHt5/YlPaeu6MT/nh5WiEclFBbBzyKpga9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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42ed173bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VfwUlAcv8OmV+vWD9YLofbakoQ6PBFWh6xE500I01QCUiCyK5yX7PrgN4oBDD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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42785f6dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uRkXAPsDe6PBvEm+wY+mHu+TgkzoKn717UnzJu7tl8dLeARPmzj90WqIQdqgI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42ed9dbe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 2000 - 1.8226084742 0.347263713816 [ 0.076855    0.40378514  0.4036386   0.40347314  0.40392923]  -  1.32133656351 1.09193542366\n"
     ]
    },
    {
     "data": {
      "image/png": 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HFbKLUHFXg3Zy2+b3DYn/W/363X6fBf68C1DREFJINZPDG1xV7Qgi9SUXHyxL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\nrsUClwUTw4ZhGIZhGONBReuvCvbkmti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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42a4697250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZO81ZYC/bbW5pnQZ8H3h3wQd2KVZ0fZBn675NmpouJ1VfL6rhxpQg5glOAu8F\njkB7GhYTjXIfNnP3TfFvl+5M1jQUnrlv/YNJ98gt1e7N5+6ueOGxhNvwcDK+cRDEfaiXLXjkdqBi\noxMV849YWMQkIUptFn5f0IFwi9H76HJUeM5FhfBs/31+bP2Q57rBf5ahnuEFqIhtRK+DIG5Dzuog\negf8JwjfSv89jXqXIbpe+mPbtQN/Q0X4y2L/Q3uWQXyFpX8bASaGJwfZPGm5GLYX9/jj3VVr10o4\nnmWTMEZKLg/wAFkGHfXLzE3NLa1nAmuA9wAXF3vAmoFn+g/seleyJr1+w/Rdt3/uvunP/GH1qqaO\nobc0phLeExxGrJ8NvAb1iGXLcTokc/ZJseiglDx7f6V75yUdiWWHpYoOq/jTN+rS9/ymNt3fI9x/\nTXW6d7fg0gIqPAaIPMPBg9fl2/soel1VEQ2sM8od9fouR2NxIWRV0IIqIbZ3OipqK1BBuggVpE1E\norUVFcop9MUpDGybT1QePB6yE4RuNWp3qdj8HtQOw0C6fv/pi322ob0UzwOP+4p168leqrnw9G8j\nxMTw5KBQb++Ivbhe+Jr4NUpBLrutQG11UA/EI/V/2YoOihsul/Qkln/m1OOe2+NNO3kEOzMmJz5D\nRCgk8FrUTGYzzLjgmoY0H728PVldP/w2/fQj0waeubtqj932dAwKJw75gxOoIOlHByc9jAqeGUT5\nhUG9fRuH3xpj3FFvaQhzmI3awGzgNLTnoh0NlaxHX4ymEfVy9KCCt5bImwtq392oiA5xwNle/uLV\nEkPO7HRsfndsWY//9Pt27PZt20g8HVq2AXGFpn8rEUOKYRH5GRof9ZJz7mA/bxbwK9Sdvh54u3Nu\nR6kbZxRMrljeVtT4zItrTET2sts+mUel275BSF3QXbHiv9sqT10ws//GF5+u+8lzvYl9jh3Bsd63\nelXTFSNrrjFZiYVE7IuKiZNQb/BCCup1c0yfl2bnVtUI+7+6T5qWDMgTd1SlP33NjhE5nS56zexU\nX3dOHT6AegRfIhq1/zA6gHQA9WaHOM1udABV20jaY4wxmQPgVAgehIrhJeg9tB71AgcHQ1wgJ4iK\nvlSgHtvgKY7H+oYc2SHrQ65wtUGtY3DYBP64O2Pzt/k2tKJ22oLGLD8+xL6HTv9WQgq5SC8F/ge4\nPDZvNXCLc65ZRFb76fNL3bipTJGppXLF8n7cxK8xlgzXbtMkeaThJroSB4Pe3K8MK22suXAhKkqK\n5UNoDtiALoGKAAAgAElEQVQ1WG+GwV4ZIUBFRogBXgK8DjgctbeC4oLrZ6X57M1tWZ+lbzlv6IwQ\n2bj1J7Xpg0/sq7jp+3UDeYRwGhW4bWjZ2xCH+Sj6//Wj3eahG70WaHfOvMJjykhiXgcPgNPeCZHn\nUfG7ChXAVWjM7TwigZv06yRin2CLaf+3wn8EFcop/z1ULCyEEKITwm/6UdtLoaEQvejAOEHzBj+B\niuH2As5FrkF0ozK4bkgx7Jy7TUSWZcx+K3C8/34ZOkLVxHCJKDa1lMXyGhOBYu327unbftWYuuvt\nHYkj3orkqoUxIn62elXTj0Zjx0ZhxMXnSAdtZQxoSxE9FAvaf0Yc8D6okHCoAF6ChkbUUMBzsaYh\nzXu/1pHY78jcOYBHwk3fq0/f9L369BCr9aMesqeBG1Hh0U10XtpQr/E89H/diQoRY6wYScyrDoJ7\nBfqyti/q5Z+F2uh21E7noIJ2JmrXlURe4AQqQkN4TfguGZ9AsTfhNNGguj60B2InURW5l1AB3Oqn\n70LDIwp7KdBY4nYGh0oUIqKHxXC7b+a5KCHyFiIX/l6IyDnAOX6yKdd6xiByDSz69tq1klXwZovl\ntdLJI8Nst2gKstt+mXnh/dOeqgZ+1JE8ptRt6ERv6l+dqrmDJ4rdxsRnmG53jmENfontaxE6Gj4M\nxulCvZ959++FdHz7FWh2iBVEBTOGZNrcAd70id2JQ08tLgVaIbRvraCq2nHleY0DQ6wavHDb0Hyv\nj6LCOMRqhm7kkC1gK1F+2QmdUm2i2G5JGBzzGir9NSDSmlXQ6fr7EYUnNACvQl/SwotaKJ6yBBWd\nQRyHyodJBqc6g8GCdyR2G/cCx+PT06gQfgkVvlvRtH6gYZobgXuHNfBNq82NSTYJcW7otC7eM3xd\nLGa43TkXu8nJDufczAL2c59z7ojhN3fykE+orl0rIRh9KLqAD2YTuFm8dHnXLxfGy4bMdiNy2e5Q\ndpummnunbxqNJvUDP0DFQTPA6lVN/aNxoJEwHjY0Vsf0g85mAW3OsdGLz+VZVn0m04Prt12Cirl1\nzrEzI5xhGnAcKizmop6wBv+3Dfg7+tCdhY5Q70FfiKpRj1Q/KoJPAg5BPW2LKNALDLDfq/rk7B/u\nGkFZ5ew8uqbKdbZVuKf+VukeW1vlKpKQzp1oIo0K3CB81wPr0MFyz/nvNUQpqlIM/v9G8DIyeW13\n1BCZj2ZyWITaa2AL8Bhxcaelj09BPb2hsht+ern/GwarxV/yg0AOy2BE5b+zEkRiCn0JS/k2DqD3\n3E7Uzp4EbvFt2YpeeyGH8IOjKWRzUYwNDdczvFVE5jvnNov+4C8Ncz9TkgK6k3MNiMukDrjSe90y\nvb5WOtkoOflslzx266golRA+CTgd+Lo/3szVq5psQNAYkhn6IMKb0d+9F+gW4UXgBdSzF89/CjBP\nZFA1rMPR2MfgDWsV4Sk0znAe6hk7CBWCc1DR3It6nrr8evuiAlFQ4dFDVBCgDhXRC9Cu5Kpi/98D\nXtMnZ3535EL4so9PG1h4UErW/l9tWgQkAf0Z8cDp3H0ZoZTyI0QZAJ5GxX8SFViZvESUlWWvMJJS\nhrAYWekiyt0bmIue85lAEpFNqF2fiHqF8csbiV74ZqLXRwhriHtnQyjEsGLTCyQeExwvqtGNpmIL\nUQJPofbZk2UfY15RrliGK4avAd6PemHeD/yxZC2aGnybHELVi4pik/Bki8200snGaJDTdoHrgI/g\nvcM7E6/h6bqfkaqYVfRBDtj9HmambiRNko7Eq9lY858s7r3EvfXYv94K3Bpb1YTwGBATTnOJPTdE\n2BfY30/WoA/JpWjoQiMqXLehA7v2QR/aCdTbW+W3CXlv5wJHoqWO21FhuwgVC7WoNypkTAiDdcIA\nstBdHLqIg0BIUqRQqEg6Xvve7opTP9ZVtMB46s5Kd93X6ge2rU+QqITjzuiuWHFMn1zxqWkDXe0V\nPHF71dBdsdnpRQVvGIGfQr3Bu9BzNQcd9BfCIDqJvPB7iZBShrAYOdCY114/NRu1UdCXxP3QF7q3\no9dJPfr7hTjxYO+gNhwGwIUcvmNBiAcO19smouwljei1t5mosMudqINibpZ9TejwHCgstdov0MFy\nTaJvMRehIvhqETkLfTN9+2g2stzJ6FbeTu5YqCXsHdoAUfxNY57DZHp9rXSyMWKKtN0P7K54uTzc\nuLbo40xL3d69K/nam4FfHb1zzsV4260gxfSB25i++zYw2x0XMgaerSASYvWoZ7eOKGaxGhW6Iddp\nDfoA3YB6Z5f6ea3o/awW9RAfgAqEeF5TQQVzZtJ/iERxo29bJYPznxb5PzoOfn2fvLu5o+jtb/95\nTXrWwrTc9P26ga3rokfqQD+s+Wldes1PC62HlJPQ1dyFnt9WovK1XajHeCV6TrpR8btn8F0WT37W\n/K0iTDcPcQnRWNc2dIDmTPS3m41eH0+h19Ii1G7rUTsPBlSD2vIA0WC4sSQMUA0e4M2o1xdUj7wM\ntaF+tAfiCeBJnNuISBVjNOitlBSSTeJdORadVOK2lD3ZYin9orjAzTcoIM3eQhj0hl9IDGTc65st\n3ZoDlqxdK+uxwXSGJ08McGZIxF622y+zWFf7Hdor3yBkt90hWdr9Geb1/azmxOP7/0nbg8Nsd8zI\njPfNWBYXTvugoQs1qHgFfbjvQ5SeKWR7aEQ9wmn/fTHqMVrk12tDPU3T0dRRs4i6gsOI93ye2fhI\n+ELyoe7F0sP65QP/szNRPQKt+r9nTB/Y9EjlcL29hRJeCmagImQpem4eJ3KQbETPoUPjUSuAg0TY\nRoYHmNxeugnflV02RFkk5qE2X4We22r0OmhAz3c9UY9HSGsWf7EL88eCMECuD+2FCKnRnkRfwGYQ\nvWRtQUOhKoD7gD/HCmiM2aC3UmIV6EpErlhK9q6klY98N/9C0p7s8ZxlSbcG0UWVN+WVMXUYIgZ4\nr7hzB2ytOpP1tV8d0XGT6W009f+eOX2/oj79EJjtjgsinIB6bMP0i86xJrZKHfrgnoV6tJaigiyN\neiSn+/UWEoUphHLaYZBN8Co3+v1V+P01+eVNFJfbdFgkqx1n/2BnYumhxZdCjvPomir30rMJd/vP\na9Pdu0YzVHMPFei5nUcU9tHr5/Wj3rsQC91L9KyYhZ7XTuLZDOBZvzzMC3HdE74ruyzQlGjL0Wvg\n1ahXOIQ4zESvmXDdNBKFPtQRxQDHK7yNlPByOdQ6faj9tKHidwfqwX7Cf0+g4TgLiOKC16Gx6xl7\ny1JRboJjYrh05BqwVqgQ7iC6GIbDXqWWQ7o1703LDJmwwXQG5B9ouaenoU/m0Zk4nKfqL2ckrOx8\nM/UDD5HYkwUKMNsdF7xHeEHG7AUiLI55iPcDjkUf4stQ0VtFVHGqFw2HqEaFlSPKf1qLPmDDYKAq\noipY+G1CBpJRE8ILV/bL4af1yqvf1TNs5fr8Q0n3i/MbBzq3VzAwMi09XIJ3eDoqgBPouRc0XKIW\n7c4Ov0Mn+qJRg/7Gs4jyEPf69eO//YsWIlECNCvE4WjWkgXodRDyWe9Gz3sV+hsOEBXGSDL42igV\njmiwXTbC4LgUKl53o7bTjfbsBO/ws37+cqKXr+1EQrjsexVMDJeOkQxM6yWKuSuGMGJ6qBzCNpjO\nyMUgG3DAgMwg4TqWbKi5UDZXf2REO1/U00xnYhVJ184+3eeTYHdYZLY7/oQBPbVEaci6/fyNIhwK\nnIqK4HlELyXb0QdoyHk6n+ghH8IcHNHguCRRPGT8YV9BCR/+iaQjUeWon+F42+c7E/seMbKCGL++\nqGHguDO6E3f+siZ9729rhyqAMdqE/yV4fePlc4N3F1SwrEdDUBrQXMoHoOKrzX92oKJnE5ENpC1m\nuEByhQCoED4RzX5yCHpug1c/9JKE3wy0p6WCwWESpSYcL+2PFV4+HVFWiNArsAV1ynWiHuE7ieLV\nX8K5zYiEwa6ZWWLKvlfBxHDpKDQdWiBcEBvQt8N8scR9fv14edBicgbbYDojFxuApQPUs73yn3i2\n7jth/ohuzId1HElN+jkw253ItBGlegp0AW0+Vvhg1CMM0UO7BhXNDn15Dw/ZEG8YBv2Eh3sXKgqG\nPbhtKGYtHOD1H+lKHPbG3hGLiUdvrXK/vqhhoNdXUX7g2pqJUrgljOzvJyo2EjzE/Qwe+R+KdiwH\nXol6J0EF8KOoWB5Af5fgMa7zf+8e9f+kXMgmenNVlNN1D0bP+SLUGxx6Q+I6K1wrDUQDTkerZySN\n/qbhGk3G5ofY4A40JOIhVACDvuw+mLEvFbtlPEBuKEwMl45sA9byIccf7wT2FNnIxfNEXcjDrSaX\nrW17dU0bU5ILNlRfcOmLNZ8ccT3k/Xe/j1mpG+KzzHYnNruIBrj1E2Us2EWUISJkcwixqSn05T3k\n9d2JepNrUO9wuJeFPMBpv7yOaGBQSaifleazN7eV5Bl28cmzUp1tYxL/WwyZLxq9qFDpQTNw7PTf\nQ9d26N7uRYXWDKKu+VAxLAxynIl69ANdwCbzDnuyiV4VjYuIvOltwDy/7r7AYcDL0Zj62UR5gMNL\nYHixCj0qo50fONhNh29DPSqAQ7z/LuAB/7nbr7cVdczlFrtlOkBuKEwMl4gsg34K8fgGcnm/nj/+\neLcsNj2sGMkcbbMR+QZ3T992DsXXpAe4FFh99M459zhY6qimgt74crPdic9B6AM+eKq2AP8gqvy2\nBX2IhnKvoexqKPrQg8YLp/xfhz7oQy7SHX56F9HAoGpKIgDcsIXw1Z9rGHjoL9VuICUkqxypPhi7\nAfuDCN3mmV7zNFGRgxDP2YnGcG5Ef5sXiH67cI6Dx7iLKMtEHyp8wgC7WlT0ZJ67cALKPvZzxAwu\noxxYhMbOH0AUOrAAvTYEfbFYDHvS2NUQDZoL53bUekeykCK6PrsYPLCyB+0hWAfchtrWizgXimfs\nHFLsluEAuaEwMVwg+conB8Kgn4xtrsyxy9bY91H3fmW2zZga5LPb5pbWfdAcmAUxo/9mZvf/nump\ntWee8rqtl+n+uUDgx0Kv2W4Z4cMgqtF7Tiir2ouK4pCPNhS0WESUVmmH30Xogg3Cy/llFajXOAys\nS6CD7lr9/CZUKASvZ9hXXDSEQXg5eeeXi8sH/Kdv1KU3P5V06+4dXPQi1TcqIjjEaIZqYSE2WohE\nbihU4FBPY6hSliI6t8+j53AaKlhaiWJ+7yQaaxJCWQI96O+5L1Esceiuf8J/5hN5/UN7apgEsZ8l\nILN3dxHq8V2EnrcK1AMfimNVoN7gOUSDRIPXN25gYyGEQyxwNzrordUfdxv6O4fPP4CW2HaDf/dJ\nKHaHwsRwAeRJP/Vq4M3k91hl1ocHfSh8PEyY98sYDXLZ7S1r6ysea7jm/SQOPTnf9uL6WdD7XRb0\nfic+8O3G4493l4UJs92yJZQpDt2+3agneB2ACPujouxWVFTN8tPBu9SBPlS7/bwdqHdyJpEA3OrX\nG/DH6/HrhkE4YZR78ISGAh2gAnAvpTpr4QDvuLgjseQV+VM6PPdA0t33x5r0A9dWuzHw+mbG6wZv\nXAhPCCKoBz1PLxGlrhpAXxb29evsIhrg9jgqeBeiwuQlv6+dwMPOsdEXRDmYSEx3ApucY50ve92I\n/iaVaOGEG4gKnrzE4FLBW6ZEiMTQXfxxYdiAxtU3+k/IERxi4sMLYBDCoQdkNI0uW6q00IPQA7xI\ndC1vRL3VaVR3PO//j+2xbSdFzO9IMTFMQV7fXOmn9pSeJXv+0y+T/RzvHMqrbBhDUazdpmikO7F/\n3bbKd/xod+LQvQoVvKz3B9/YUv3h84D9XrVzyU0JurNlbDggc4bZblmSBF6FZomYjT7IpwH3orGP\n89GH5hL0QV9P1P0bfxDPQEXWJqKQiiaiAXdtqCdyP1REhPLZDhXSIayi3h+nkigrxR6alqYYSAmf\nvnZH1mfWBUfMTlVUQNPSAbauS2RuPlyCyA1CAv9/BQdH8PyGstDbUQ9cC/oikES71uegAnkjWqBg\nF1rCOoiTtF83hKKEggbdftt4VbIwij8F4EVvK/o7AmwNgtY51ojwDPobdgPrwjJffAOiXMNbnOMf\nIzxfE59cA+DiaBnlFOrtrUPtsd5vN9t/D70a9UShKmFe/AWoVLjY37gYDqE2/ehL0ouoR3gLGgrR\nhYZz1PrvIWXaA4QqcyaEARPDeYsOxIRFrjROmXfczPynubabPczmGgZQnN2+UPUfbKn+EP0V4XmZ\nvWLXsp7P/cuZR3/2XOCptWu7F+c4tKU0mxzMQQXvoajnKIXel1LoqPLZ6MP/CFS4xQWqoII3hXow\n5wAHEonEILBCUYgwqCsIip7Y8cIo91COdo+IqKp1vP1LHYmXn5A/luGq1Y0DLi0MpCFeDnkYhBH2\nbahXdpP/BG/2FlRYLPdtXYAK2OAB70BfJp7227UCN6OxpF1+n2Fw4h1E1+HWWJnkPWWTAUTY6o8H\nOVJZ+XWzChqfL3pjlvnrsh1vUpM9FngGItO9AJ6OvlQsRu0zgXrVa1A7b0DtNPxuaT8vM11gqbzC\nLuMTBrHG0+uFkKRQKONR1Fv9nP+0o9lDZhHFOm/Cub1sYqoz5cUw+YsOBFFRTNq0uFiwtFDGXjS3\ntM4G3gfcs3pV013D3E1Wu+2V+V9pbmltAp46isSGTdX/39IXas4bcmdH75wDZrtTiSY0DnIJ+nBN\no6K4EhVf1ahYnkesK/1lK1KsOKav4sHrq9Md2xKg3uOX+cVhtHyojhYyIcTjdONiYVB376KD+2XZ\noSl58m+V6d07KvjcmsIGyD18Y/VwyyGHkIxdaAnjdaiQ2Ajc7xx3ZG7gwxKOJKrINxsVwS+gguk5\n4PGYuLzff+LkEq57iVovktvJGN1fCvGaT0RPUuL3y3j1vTpEmtBwkznofa8RfcnZgP7Gy4iKZ4R4\n92qiHoIQDw6D7b1Qwn4hEtchZV4/+iIUMrg4okwtofjFM2jZ5A3oi1h4cUqiL2Hh/zdPcA5MDBeW\n1L+YtGlxsWBpoSY5zS2tlcAJwJvQm9TNwJrVq5q6YutUoUnYD0UfuJeiN1eaW1rnrF7V1Nrc0hrK\nctYCL61e1ZTzhtrc0po8QmYs6apYScPAfVTQ5xVHNY823LAI+DbAPdO3FPQ/HLD7neGr2e7UYV7d\njPSilcf3NS45pL+yfWvCPXlH5cCLjyfrnJOFqC021jamKxcclJLp89KkB+AdX+pMABz2xt6K775r\nZgqgboYuw5Hs6ayAwc+VQV6yZLWjsSlNTYNj85MJCc/2+fsP8NHLdyYATju38GwTFx07q5g8wA4V\nP+tQj9kA8DBq5y+QJdRgrx3sHZbQTYaHt4j2FNboqejFHR3CPXkRKnhnox7/Wei5XUYUNhRirWeh\nIngu0cC4AVQIh9zp8R6TNMV7hoPg7ScKuQi5gIPndwP6ohYqDO5AX8aC13o72qOzPsv+63ymCLOb\nPJgYLsADljFIKJ+HeJBYsMFFU4JzgUti058AeptbWtegHqZQmrMqy7YAn2tuaU377QJ9zS2tX0Nj\nD6cBf1i9qqmtuaX1X4DfANw3LSoHX596gN3Jw4fV+MN3HUKV2wJmu1ON2Wd9b+fcBQcO7Emr9/oP\nk+zYLtXP3FNVl6xysuCAVHL24uwp0BccMMDKE3rl6H/tqVhxdFTpbXe7cO1XGgaSNY6uduGJ26uc\nS8NbV++uOPrte5dDbt9awYx5wyvu9pkjZ6fSucfRBa9zGFm/A72eQlWZAWBDrOw0FCgWxsOjOgW9\nuKUnigU+En2Oh2waRxJVSmwiyrBRiYbCOPQ+HO7h8UIaofcj/A3z8hEGuiVi34OtptFQjFBhMIQi\ntaHx5d1oT0wHKtgTaPjOLUShHPFwGrAMIQUhzg23h2kYBxO5zzl3xJgdsACyxF5CngpZvkBGrjvw\ne0wsjC7jZUO5jtvc0nogUTdUWXFIx0nUpx8Kk2a7o8x42G6uY4rwHyee0/WV13+4K2v8+ETns0fN\nTg3sXW25F30BfQwVC9PQru6tqJh42DnWjGU7JwsTyXaL3Mli1Lvb5qunvRJ4J1GKv+n+04u+IDUS\nhfJ0ol7/JFE2iZBRJQysg8HiN8Qa59IIA0QvaCE+vZWoEl2NXy9UF+xDY9AfQbN/9KJ23YCGdOxC\n44Q3+e0qiQZ7gmaKGDxAcApRjA1Nec/wMDxg+QpkmJiYYqxe1fREc0vrDehbez9am35lllVDqdpx\npX7gH8zpu4q5fVdRsScFqdnuFGT7wzdW9R94bF/N+paka5ztZMUxfVI/c7BzJNUPyRHXJiwNd/6y\nJv3M3ZXu8duqsqVLGwC+AfwSn8XCpx7bI4YyvMDGZEfkBNSzG6bb0XCHxaigBPXC1hB5aavQF6kQ\nujAf9uTkDlX8uvy68ewRFbFt4h7iIKxD1oeQ51cLXWicr6CiNuQuriMSy2FQ5kOE7A/KfqgOaWOw\nJ9jig4fJlBfDUHRqKIulNAaxelXTG+PTzS2tS4E3oDfcB4EHfJjDCcA7gA+NdROB7n27Pl47t/+q\nCzHbNYBt65O93ztjxh5bkArHwpUp2ffwftfbLWx6JMmWZ5IM9MNr3tNTMW1OmuPO6B7TmsXXfb0+\n3d+De+SWatfVnvfQNzrHhZkzc2VTMCY56hEOKcWqUUF7ov++L3pv7iYqLx5yQCfQ++NG9KUqiOD4\nALl+VNyGNIMhC0qI7w1VFtNEHt/gDW7zn61o7HqXP94mNNyhgqgCZJdf98EsovYBRHaSu2yyieAi\nmfJhEoFCKswNZ12jtEy0MInh0NzSOg+4Gjguy+KHgK+gccjPAV9EB+UBrEEH6+XHpQeQivrVq5p6\nMxeZ7Y4fE6mrWYSzgAtRz1emm7ULfbhXZ2639LB+Oev7OxOVey2Bv15am66scRx6am/FXb+sTdfP\nSnOMjxPe9FjSLVqZv1AGwN9/X+1+98XGgaHWy+B+5zi6yG2MIphItlvgxoei4jfkxl6KDpzr8PPm\noc7A4OENpcaDmH0B9bgeSJRnG1Tw7kAHYDagQjgI7uDxDQVj+v28hD/WDlT0rkfj1/9BlLc4eHgX\n+f22+k/+MIehC4hMaYqxIRPDFB83bIwfk0EMx2luaa1Ab9Rb8aPds2WSaG5prVy9qqnfZ6ZIrV7V\nlG5uaV2yuOdLZ/dL0392Jg5Pzu/9PrNS1yFmuxOSiSQoRHgn8Fn0pSikhwrpnXb67zPJPfCTZJVj\n+rw02zcmSFY7Ur17a92KhNNMEwjJKren/PHClf1SU+847v3dFQMp4dqv1g/seGFYUURPA8dYhoXR\nZSLZboEbHwn8MypIG9C0afOIyhLPQEVwFypCk6gYbkfFaSdaTOZQ1MMcCm2kUSfC4379fdH7t0MF\nbRdR+MRuf6xa/+n1+7wbuBfn1nkxG/JIBxr8eltN4I4ME8NFsnatrCd3HPCysW2NkY/JJoZHitlu\n+TCRBIUIK4GvodXmqohKCYfiEn2ol6qJLB7iCcKDwNlTonLaODORbDe2QnavqFaZW472vC1Bhewi\nouIyXUShEcEJ0Yd6g/tQMRqKVaz0n1BAphO4E7gWFb9v8MeqRcMgEv5vKDXe47dtQwfAPQ6sy9Le\nzHCHKTvorZTYALriKSTXsGFMRMx2jaJxjsdEuB71/k73s3egguBp1FM8G007tRx9VpSszvEwSROJ\n9d8CvzAhPEXJVVY5qjLXg4rZKjQV2S40BrieqIhMKF9cSZQtYjvqlW1HPbyhGEsKDVt4EnjGp2mb\nj4Y7bEMHtIXMLH1ozt86dPDmdvSayi5yo3ZbuMM4YmJYsWpbRrlitmsMC+f4rggdwCvRh/1z6IN7\nE+rNakRFxE5gIVHVrpBndTQH04WQDUGFzVNo9/LDwFpGqcCFUQbkLqscMoeEXLv9RGEP09GwhTrU\ndvtR0duDitmlqK09h3qOpxGFPbShJYwzhWzI7LDJH2eWn76PqOx2iEvOL3J1mdnzOGJiWLEMEUa5\nYrZrDBvnuFSEW4ilH4tVO2tERcNTwArUUzwNfW6EylwLiGIpw/MkDMCr9X8TRKWPw+j6QD9RsYGd\naFfyLqKQjfXAn/y8zCIZxtQkWyXYENLT4793osI2iXp+Q/qz6WgYQwhd6PTbPEMUT1yH2m6dX96J\niu3pgwSteodDqeywXjvOBRs1cVtGmBjGqm0Z5YvZrjFSMtOPhWpnInShgrgdtase9MFfSVSO+B9+\n+hC//CW0W7oSzeda6+d3APugz5waVJjsRGMonwSewHt7fTzzfGCzczw2av+4Ua5kVlRrIIrzDaI0\nTG/z0zvRF7jdRNXbOtHQoJBBosv/DS9uVbF9d6LieLDAtRCHSYOJYU+RuYYNY8JgtmuMBl6YtvvJ\nkNh/Exo7WQd0xUIVBlV2897lg1BxEcTJjcDjfr/Ts+wjHPcxMBFs5CDyyC5CX6ziHlxQGw1i+EE/\n7yBUDIfiR0EAV/vt64jSowXC9xq/7+xljS3EYVJgYtgwDMPIinOsyyFc8z78/Xp35xK9wfs8Ss02\npha9aE9EnE5gfcxTe/deHlytUDfTL29EhXJ4+WslEr+acs28vpMaE8OGYRhGTkYiXE30GiUnGkAX\n9waHYhVhem/xGvfg6j52obHqNag3GaIBb6E3oxd43ITw5MfEsGEYhmEY5UK2AXSb0FjgDgqL3Q37\niAtq0FRroUSyxQBPIUwMG4ZhGIZRLmSP3S2uYluufXRZDPDUZDTzRBqGYRiGYZQOFavtGXOLi+kt\nxT6MScWIPMMicirwbXR05k+cc80laZVhGIZhGEY2SpHSzNKiGTGGLYZFJAH8L/B6NF7n7yJyjXPO\nUuIYhmEYhjF6lCKcwUIiDM9IwiSOBJ5xzj3rnOsDfgm8tTTNMgzDMAzDMIzRZyRhEgthUGnMTcBR\nmSuJyDnAOX7yABG5bwTHLJYmNF9gOVBObYXxa+/SsTrQONqu2cLoMqlt1+65RWHtLQyz3YlFObUV\nyid9kUIAAANaSURBVMBuxTk3rCOIyNuAU51zZ/vp9wFHOef+fVg7HAVE5D7n3BHj3Y5CKKe2Qvm1\nt5wot3Nr7TUC5XZurb1GoJzObTm1FcqjvSMJk3gBrT0fWOTnGYZhGIZhGEZZMBIx/HdghYjsIyJV\nwDuBa0rTLMMwDMMwDMMYfYYdM+ycS4nIvwN/QVOr/cw592jJWlYafjTeDSiCcmorlF97y4lyO7fW\nXiNQbufW2msEyuncllNboQzaO+yYYcMwDMMwDMMod6wCnWEYhmEYhjFlMTFsGIZhGIZhTFkmtRgW\nka+KyBMi8pCI/F5EZox3m7IhIqeKyJMi8oyIrB7v9uRDRBaLyBoReUxEHhWRj493myYjZrulxex2\n7CgH2y0XuwWz3bGiHOwWzHZHi0kdMywipwC3+sF+XwFwzp0/zs0ahC9r/RSxstbAuyZqWWsRmQ/M\nd849ICKNwP3A6RO1veWK2W5pMbsdOya67ZaT3YLZ7lgx0e0WzHZHk0ntGXbO3eicS/nJu9FcyBON\nsipr7Zzb7Jx7wH/vAB5HqxEaJcRst7SY3Y4dZWC7ZWO3YLY7VpSB3YLZ7qgxqcVwBv8PuH68G5GF\nbGWtJ6SxZCIiy4BVwD3j25JJj9luCTG7HVMmou2Wpd2C2e4YMhHtFsx2R41h5xmeKIjIzcDLsiz6\njHPuj36dzwAp4MqxbNtkRkQagN8Cn3DO7Rrv9pQjZrtjj9ltaTDbHXvMdkeO2e34UA62W/Zi2Dl3\ncr7lInIm8GbgJDcxA6TLrqy1iFSihn2lc+53492ecsVsd2wxuy0dZW67ZWW3YLZbKsrcbsFsd9SY\n7APoTgW+AbzOObdtvNuTDRFJogHxJ6FG/Xfg3ROwmh8AIiLAZUCbc+4T492eyYrZbmkxux07Jrrt\nlpPdgtnuWDHR7RbMdkeTyS6GnwGqge1+1t3OuQ+PY5OyIiJvAr5FVNb64nFuUk5E5FjgduBhIO1n\nX+Cc+/P4tWryYbZbWsxux45ysN1ysVsw2x0rysFuwWx3tJjUYtgwDMMwDMMw8jGVskkYhmEYhmEY\nxiBMDBuGYRiGYRhTFhPDhmEYhmEYxpTFxLBhGIZhGIYxZTExbBiGYRiGYUxZTAwbhmEYhmEYUxYT\nw4ZhGIZhGMaU5f8HhSRk9DkkwHYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42edb6f390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WJmEYhmEYhmHMWMwzbBiGYRiGYcxYJjTPsIjsIn+yf8MYjhXOuXyFGsYFs12jCEy47Zrd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4279ff2d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25 1000 - 1.17549462592 0.0491106697204 [ 0.06876557  0.40362921  0.40344572  0.40309581  0.40392563]  -  1.35654852785 0.819570441895\n"
     ]
    },
    {
     "data": {
      "image/png": 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W+tdfLP3wDMiYSNSMGti5cU9tjqYYHycy0iCgbwZ+2NIiV/vt8or9NYx8yZIA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\nxLBhGIZhGIZRtpgYNgzDMAzDMMqW/x9pGk1butZEEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42edbc6ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YhmEYRtViYRKGYRiGYRhG1WKeYcMwDMMwDKNqmdA8wyKyn8KJ/g2jGFY45woVaqg4ZrtG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42786b1e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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D2s37auAVqFAoeIDmlQ/uKuq+u31tFVe/p3nwwG7VzTuePWTzXrT7+Wn04e5p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\n/r6z/bYh93CK7GEOYZvwYBM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6bU8ReXRDPuoQKpEiEsYDRKFzW1GBuxftKTwCvQdUERVo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\nDMMwDKNiMTFsGIZhGIZhVCz/D84NdiBLhPHoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f427a093d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50 500 - 1.152001802 0.0546645034129 [ 0.07132343  0.32557228  0.32549378  0.32532749  0.32589889]  -  1.26965758649 0.745415424142\n"
     ]
    },
    {
     "data": {
      "image/png": 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cnaKpOKK8FVjp3/8WaMLE8LhIM8v+CtSY6iahS33Ax/17ywxhpCWN7RaFntiB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\nMaoT4yo5b7ZrwOgsO1Wo8B1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M24QhYzJZtaKxC7jVv/LCbNcoAo3o9T/w1gZxjI3JG7a8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42f5977150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EHvL9CCoZ4pe3ANuSinmk/n8mGXFZ5o+IyGvRf+76iBj+NrDTOdciIiuAWc65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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42edce0e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MgN/uaN+2Bo0RP4LI8yuo2M2M5w3e3lB0JYRMOP+6gegmq9W3h9zWCb/tnFj7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\n1aPRsQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42ed47b290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 200 - 1.14467085788 0.0271470485769 [ 0.07868228  0.23599394  0.23589814  0.23577261  0.23628223]  -  1.24654124485 0.668062326223\n"
     ]
    },
    {
     "data": {
      "image/png": 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YiOF6VAg/XvTvIg352pF5hseAHBPhGoFrUAMtx/jgdFwz1h0wRgdvu6lCGNRW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\nmLD8/wIdAbP/Nc1gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42783c6e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YB8liu08AF5Xr+xyC4EjRzIOzHiAlbXl/9vAD/3rtC1Yk3we8r1z9M6YHGaWR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\nMWwYhmEYhmHMWP5/bG6JR4yRy28AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42ed649e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Vve8EXosKh5wOCqlz1DdBQ6PjvH/fnTjg2GTOSp1x/vMD05IuLWx5qZ6r3jM9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\nYdQsJoYNwzAMwzCMmuX/B2ZWn/xoy0T3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42a4682a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 20 - 1.06534282935 0.028514363992 [ 0.07469008  0.23062098  0.22492842  0.22430871  0.23339403]  -  1.32083792079 0.651976727698\n"
     ]
    },
    {
     "data": {
      "image/png": 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Xuu2mGf0wU7da2RiK7ceoLOLp9smPF7Bs6Iskadu2vuX8OeiD5C3nruxcW+g2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\nYUxbTAwbhmEYhmEY05b/HwXK3qft39lOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4279ff8190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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v70uo0A08ubuioRC7oN7feah4DoY8Dows1U4DL3BDynQmgmQ6CIXuZtRmOwiF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42ecfeed50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Jp07gF4GrgMO7u2JHXPfxyT2IewknW9H777K0euxwrrw8bcY4GDowxlw0xrcJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42edd37d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 2 - 1.20510557406 0.0890855681927 [ 0.07931601  0.13712122  0.12683423  0.11200676  0.16869354]  -  1.2288792592 0.54163583949\n"
     ]
    }
   ],
   "source": [
    "results = []\n",
    "# get results for multiple N\n",
    "for N, nb_epoch in zip(Ns, nb_epochs):\n",
    "    # repeat exp multiple times\n",
    "    rep_results = []\n",
    "    for i in range(nb_reps):\n",
    "        X, Y = gen_data(N + nb_val_size)\n",
    "        X_train, Y_train = X[:N], Y[:N]\n",
    "        X_val, Y_val = X[N:], Y[N:]\n",
    "        model, ELBO = fit_model(nb_epoch, X_train, Y_train)\n",
    "        MC_samples = np.array([model.predict(X_val) for _ in range(K_test)])\n",
    "        pppp, rmse = test(Y_val, MC_samples)  # per point predictive probability\n",
    "        means = MC_samples[:, :, :D]  # K x N\n",
    "        epistemic_uncertainty = np.var(means, 0).mean(0)\n",
    "        logvar = np.mean(MC_samples[:, :, D:], 0)\n",
    "        aleatoric_uncertainty = np.exp(logvar).mean(0)\n",
    "        ps = np.array([K.eval(layer.p) for layer in model.layers if hasattr(layer, 'p')])\n",
    "        plot(X_train, Y_train, X_val, Y_val, means)\n",
    "        rep_results += [(rmse, ps, aleatoric_uncertainty, epistemic_uncertainty)]\n",
    "    test_mean = np.mean([r[0] for r in rep_results])\n",
    "    test_std_err = np.std([r[0] for r in rep_results]) / np.sqrt(nb_reps)\n",
    "    ps = np.mean([r[1] for r in rep_results], 0)\n",
    "    aleatoric_uncertainty = np.mean([r[2] for r in rep_results])\n",
    "    epistemic_uncertainty = np.mean([r[3] for r in rep_results])\n",
    "    print N, nb_epoch, '-', test_mean, test_std_err, ps, ' - ', aleatoric_uncertainty**0.5, epistemic_uncertainty**0.5\n",
    "    sys.stdout.flush()\n",
    "    results += [rep_results]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "with open('concrete-dropout.pkl', 'wb') as f:\n",
    "    pickle.dump(results, f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import pickle\n",
    "# with open('concrete-dropout.pkl', 'rb') as f:\n",
    "#     results = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.82260847  1.17549463  1.1520018   1.14467086  1.06534283  1.20510557]\n",
      "[[ 0.076855    0.40378514  0.4036386   0.40347314  0.40392923]\n",
      " [ 0.06876557  0.40362921  0.40344572  0.40309581  0.40392563]\n",
      " [ 0.07132343  0.32557228  0.32549378  0.32532749  0.32589889]\n",
      " [ 0.07868228  0.23599394  0.23589814  0.23577261  0.23628223]\n",
      " [ 0.07469008  0.23062098  0.22492842  0.22430871  0.23339403]\n",
      " [ 0.07931601  0.13712122  0.12683423  0.11200676  0.16869354]]\n"
     ]
    }
   ],
   "source": [
    "best_tests = np.array([[r[0] for r in result] for result in results]).T\n",
    "best_ps = np.array([[r[1] for r in result] for result in results])\n",
    "best_aleatoric_uncertainty = np.array([[r[2] for r in result] for result in results]).T.squeeze()\n",
    "best_epistemic_uncertainty = np.array([[r[3] for r in result] for result in results]).T.squeeze()\n",
    "print best_tests.mean(0)\n",
    "print best_ps.mean(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42edde2b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6iJk9o6B0NoPQwnaaWfkARjnXErqZj0Q7/i9e6yVJFxO+jM8SuoMlpgEXSnqD\nEGqwWrmUev4cuCB2d1cAx5rZ8grjQpXq+4KkPykov90YbfiWpLcJz/2VWshOwvPpbRXyfgGcVpa2\nN5W7sk3Hl185TSO+2/uDmfWp9q2koYQfrD3MbGWdspsBl5vZPr1iXBneZXVaHjN7A/g+QZCqHmMI\nI7d9greQjlMgvIV0nALhDuk4BcId0nEKhDuk4xQId0jHKRDukI5TIP4/w5ILSJ8MX5oAAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42ed790c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xhiRpelk/TVirWDSz24FFkg5Nk3mU3aincH4I8GMLPAisJWkUYR7tZDObH51wMrBfmmc6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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42ed2175d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab\n",
    "%matplotlib inline\n",
    "\n",
    "pylab.figure(figsize=(3, 3))\n",
    "pylab.plot(Ns, np.mean(best_epistemic_uncertainty, 0)**0.5, '-*')\n",
    "pylab.xlabel('Number of data points (N)')\n",
    "pylab.ylabel('Epistemic uncertainty (std)')\n",
    "pylab.xscale('log')\n",
    "pylab.savefig('epistemic.pdf', bbox_inches='tight')\n",
    "pylab.show()\n",
    "\n",
    "pylab.figure(figsize=(3, 3))\n",
    "pylab.plot(Ns, np.mean(best_aleatoric_uncertainty, 0)**0.5, '-*')\n",
    "pylab.xlabel('Number of data points (N)')\n",
    "pylab.ylabel('Aleatoric uncertainty (std)')\n",
    "pylab.ylim([0, 2])\n",
    "pylab.xscale('log')\n",
    "pylab.savefig('aleatoric.pdf', bbox_inches='tight')\n",
    "pylab.show()\n",
    "\n",
    "pylab.figure(figsize=(3, 3))\n",
    "predictive = np.mean(best_epistemic_uncertainty, 0) + np.mean(best_aleatoric_uncertainty, 0)\n",
    "pylab.plot(Ns, predictive**0.5, '-*')\n",
    "pylab.xlabel('Number of data points (N)')\n",
    "pylab.ylabel('Predictive uncertainty (std)')\n",
    "pylab.ylim([0, 2])\n",
    "pylab.xscale('log')\n",
    "pylab.savefig('predictive.pdf', bbox_inches='tight')\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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18jOv/TzjJCkTwynIoR1uZl/ch6KdjV6KZ/z48UUOhwOHw8GZZ555bOfOnUnx1iWqE1PV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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4272efa610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.figure(figsize=(3, 1.5))\n",
    "ps = best_ps.mean(1)\n",
    "ps_std = best_ps.std(1)\n",
    "for i, (p, p_std) in enumerate(zip(ps.T, ps_std.T)):\n",
    "    if i == 4:\n",
    "        continue  # layer 4 is noise layer\n",
    "    pylab.plot(Ns, p, '-*', label='Layer #' + str(i+1))\n",
    "#     pylab.fill_between(Ns, p + p_std, p - p_std, alpha=0.25)\n",
    "pylab.legend(bbox_to_anchor=(1, 0), loc='lower left')\n",
    "pylab.xlabel('Number of data points (N)')\n",
    "pylab.ylabel('Dropout probability')\n",
    "pylab.xscale('log')\n",
    "pylab.savefig('dropout_prob.pdf', bbox_inches='tight')\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
